What do Islamist terrorists want? The answer should be obvious, but it is not.

A generation ago, terrorists did make clear their wishes. Upon hijacking three airliners in September 1970, for example, the Popular Front for the Liberation of Palestine demanded, with success, the release of Arab terrorists imprisoned in Britain, Switzerland, and West Germany. Upon attacking the B'nai B'rith headquarters and two other Washington, D.C. buildings in 1977, a Hanafi Muslim group demanded the canceling of a feature movie, Mohammad, Messenger of God," $750 (as reimbursement for a fine), the turning over of the five men who had massacred the Hanafi leader's family, plus the killer of Malcolm X.

Such "non-negotiable demands" led to wrenching hostage dramas and attendant policy dilemmas. "We will never negotiate with terrorists," the policymakers declared "Give them Hawaii but get my husband back," pleaded the hostages' wives.

Those days are so remote and their terminology so forgotten that even President Bush now speaks of "non-negotiable demands" (in his case, concerning human dignity), forgetting the deadly origins of this phrase.

Most anti-Western terrorist attacks these days are perpetrated without demands being enunciated. Bombs go off, planes get hijacked and crashed into buildings, hotels collapse. The dead are counted. Detectives trace back the perpetrators' identities. Shadowy websites make post-hoc unauthenticated claims.

But the reasons for the violence go unexplained. Analysts, including myself, are left speculating about motives. These can relate to terrorists' personal grievances based in poverty, prejudice, or cultural alienation. Alternately, an intention to change international policy can be seen as a motive: pulling "a Madrid" and getting governments to withdraw their troops from Iraq; convincing Americans to leave Saudi Arabia; ending American support for Israel; pressuring New Delhi to cede control of all Kashmir.

Any of these motives could have contributed to the violence; as London's Daily Telegraph puts it, problems in Iraq and Afghanistan each added "a new pebble to the mountain of grievances that militant fanatics have erected." Yet neither is decisive to giving up one's life for the sake of killing others.

In nearly all cases, the jihadi terrorists have a patently self-evident ambition: to establish a world dominated by Muslims, Islam, and Islamic law, the Shari'a. Or, again to cite the Daily Telegraph, their "real project is the extension of the Islamic territory across the globe, and the establishment of a worldwide ‘caliphate' founded on Shari'a law."

Terrorists openly declare this goal. The Islamists who assassinated Anwar el-Sadat in 1981 decorated their holding cages with banners proclaiming the "caliphate or death." A biography of one of the most influential Islamist thinkers of recent times and an influence on Osama bin Laden, Abdullah Azzam declares that his life "revolved around a single goal, namely the establishment of Allah's Rule on earth" and restoring the caliphate.

Bin Laden himself spoke of ensuring that "the pious caliphate will start from Afghanistan." His chief deputy, Ayman al-Zawahiri, also dreamed of re-establishing the caliphate, for then, he wrote, "history would make a new turn, God willing, in the opposite direction against the empire of the United States and the world's Jewish government." Another Al-Qaeda leader, Fazlur Rehman Khalil, publishes a magazine that has declared "Due to the blessings of jihad, America's countdown has begun. It will declare defeat soon," to be followed by the creation of a caliphate.

Or, as Mohammed Bouyeri wrote in the note he attached to the corpse of Theo van Gogh, the Dutch filmmaker he had just assassinated, "Islam will be victorious through the blood of martyrs who spread its light in every dark corner of this earth."

Interestingly, van Gogh's murderer was frustrated by the mistaken motives attributed to him, insisting at his trial: "I did what I did purely out of my beliefs. I want you to know that I acted out of conviction and not that I took his life because he was Dutch or because I was Moroccan and felt insulted."

Although terrorists state their jihadi motives loudly and clearly, Westerners and Muslims alike too often fail to hear them. Islamic organizations, Canadian author Irshad Manji observes, pretend that "Islam is an innocent bystander in today's terrorism."

What the terrorists want is abundantly clear. It requires monumental denial not to acknowledge it, but we Westerners have risen to the challenge.